Publication: Lise öğrencilerinin matematiksel modelleme sürecinin problem kurma bağlamında incelenmesi
Abstract
Problem kurma, problem çözme gibi matematik öğrenmenin önemli bir bileşenidir ve matematiksel modellemenin önemli bir parçasıdır. Bu çalışma kapsamında akademik başarısı yüksek lise öğrencilerinin problem kurma görevlerindeki başarı düzeylerini ve kendi kurdukları problemleri nasıl çözdükleri incelenmiştir. Ayrıca lise öğrencilerinde problem kurma görevlerinin matematiksel modelleme sorusuna yönelik çözüm süreçlerini nasıl değiştirdiği incelenmiştir. Çalışmada nitel araştırma yöntemlerinden ‘durum çalışması’ deseni benimsenmiştir. Çalışmanın çalışma grubunu bir fen lisesindeki 10.sınıf öğrencisi olan 9 öğrenci oluşturmaktadır. Çalışma grubu, amaçlı örneklem yöntemlerinden olan ‘benzeşik örnekleme’ yöntemi esas alınarak belirlenmiştir. Veri toplama aracı olarak problem kurma etkinlikleri, görüşme formu ve matematiksel modelleme problemi kullanılmıştır. Çalışmanın başında ve sonunda aynı matematiksel modelleme problemi öğrencilere çözdürülmüştür. Süreç içinde altı hafta boyunca da problem kurma etkinlikleri yapılmıştır. Problem kurma etkinliklerinin tasarımında Christou ve arkadaşları (2005)’na ait kuramsal çerçeveden yararlanılmıştır. Bu kuramsal çerçeveye göre problem kurmada kavrama, aktarma, düzenleme ve seçme olmak üzere dört farklı yöntem önerilmiştir. Matematiksel modelleme probleminin çözümü ve problem kurma etkinlikleri grup çalışması şeklinde gerçekleşmiştir. Araştırmanın sonunda her grupla görüşme yapılmıştır. Problem kurma etkinliklerinin analizi için Yıldız (2014) tarafından geliştirilen “Problem Kurma Beceri Testi Puanlama Cetveli” kullanılmıştır. Buradaki kriterler; matematiksellik, dil bilgisi ve ifade, çözülebilirlik ve orijinallik şeklindedir. Ayrıca çalışmanın amacına uygun olarak “gerçek hayata uygunluk” kategorisi dâhil edilmiştir. Öğrencilerin matematiksel modelleme becerileri Berry ve Houston (1995) tarafından geliştirilen matematiksel modelleme süreci temel alınarak analiz edilmiştir. Çalışmanın sonuçlarına göre öğrenciler, problem kurarken başarılı olmasına rağmen dil bilgisi ve ifade açısından eksiklikleri bulunmaktadır. Ayrıca öğrencilerin kurduğu problemler genelde orijinal değildir ve problemleri daha önceki deneyimlerinden yola çıkarak kurmuşlardır. Öğrenciler problemler kurarken genelde kavrama ve aktarma görevinde zorlanmamıştır. En zorlandıkları kategori, düzenleme görevi olmuştur ancak burada bir hiyerarşinin olduğundan bahsedemeyiz. Öğrenciler kurdukları problemi çözerken genelde başarılı olmuştur. Problem kurmanın öğrencilerin bakış açısını değiştirmek, kendini ifade etmek, yaratıcılığını göstermek, eğlenceli vakit geçirmek gibi durumlarda katkı sağladığı saptanmıştır. Ayrıca grup çalışmasının iletişim ve karşısındaki insanın fikirlerini anlamada olumlu yönde etkilediği görülmüştür. Son olarak problem kurma görevleri sonucunda matematik modelleme sorusunun çözüm süreci pek değişmemiştir. Ancak bazı öğrencilerde problem kurma etkinliklerinin matematiksel modelleme sorusunu anlamada yardımcı olduğu gözlenmiştir.
Problem-posing is one of the important components of learning mathematics, as is problem-solving, and is an important part of mathematical modeling. Within the scope of this study, the success levels of high school students who have high academic achievement in problem-posing tasks and how they solved the problems they posed were examined. Additionally, how problem-posing tasks changed the solution processes of the mathematical modeling question for high school students was also examined. Of the qualitative research methods, the 'case study' design was used in the study. The study group for the research consists of 9 10th-grade science high school students. The participants were determined based on the ‘homogeneous sampling’ method, one of the purposive sampling methods. Problem-posing activities, interview forms, and mathematical modeling problem were used as data collection tools. At the beginning and end of the study, the students solved the same mathematical modeling problem. During the process, problem-posing activities were carried out for six weeks. The theoretical framework of Christou et al. (2005) was used to design problem-posing activities. According to this theoretical framework, four different methods have been proposed for problem-posing: comprehending, translating, editing, and selecting. Solving the mathematical modeling problem and problem-posing activities were carried out as group work. At the end of the study, interviews were conducted with each group. The “Problem-Posing Skill Test Scoring Chart” developed by Yıldız (2014) was used to analyze problem-posing activities. The criteria here are; mathematization, grammar, expression, solvability, and originality. In addition, the category of “suitability for real-life” was included in accordance with the purpose of the study. Students’ mathematical modeling skills were analyzed based on the mathematical modeling process developed by Berry and Houston (1995). The results of the study show that although the students are successful in posing problems, they are poor in grammar and expression. In addition, the problems posed by the students were generally not original, and they posed the problems based on their previous experiences. Nevertheless, while posing problems, students generally did not have difficulty comprehending and translating tasks. The most challenging category for them was the editing task, but we cannot talk about the existence of a hierarchy here. The students were successful in solving the problems they posed in general. Furthermore, it has been determined that problem-posing contributed to changing students’ perspectives, expressing themselves, demonstrating their creativity, and having fun. In addition, it has been seen that group work has a positive effect on communication and understanding the other person’s ideas. Finally, as a result of the problem-posing tasks, the solution process of the mathematical modeling question did not change a lot. However, problem-posing activities were observed to have helped some students understand the mathematical modeling question.
Problem-posing is one of the important components of learning mathematics, as is problem-solving, and is an important part of mathematical modeling. Within the scope of this study, the success levels of high school students who have high academic achievement in problem-posing tasks and how they solved the problems they posed were examined. Additionally, how problem-posing tasks changed the solution processes of the mathematical modeling question for high school students was also examined. Of the qualitative research methods, the 'case study' design was used in the study. The study group for the research consists of 9 10th-grade science high school students. The participants were determined based on the ‘homogeneous sampling’ method, one of the purposive sampling methods. Problem-posing activities, interview forms, and mathematical modeling problem were used as data collection tools. At the beginning and end of the study, the students solved the same mathematical modeling problem. During the process, problem-posing activities were carried out for six weeks. The theoretical framework of Christou et al. (2005) was used to design problem-posing activities. According to this theoretical framework, four different methods have been proposed for problem-posing: comprehending, translating, editing, and selecting. Solving the mathematical modeling problem and problem-posing activities were carried out as group work. At the end of the study, interviews were conducted with each group. The “Problem-Posing Skill Test Scoring Chart” developed by Yıldız (2014) was used to analyze problem-posing activities. The criteria here are; mathematization, grammar, expression, solvability, and originality. In addition, the category of “suitability for real-life” was included in accordance with the purpose of the study. Students’ mathematical modeling skills were analyzed based on the mathematical modeling process developed by Berry and Houston (1995). The results of the study show that although the students are successful in posing problems, they are poor in grammar and expression. In addition, the problems posed by the students were generally not original, and they posed the problems based on their previous experiences. Nevertheless, while posing problems, students generally did not have difficulty comprehending and translating tasks. The most challenging category for them was the editing task, but we cannot talk about the existence of a hierarchy here. The students were successful in solving the problems they posed in general. Furthermore, it has been determined that problem-posing contributed to changing students’ perspectives, expressing themselves, demonstrating their creativity, and having fun. In addition, it has been seen that group work has a positive effect on communication and understanding the other person’s ideas. Finally, as a result of the problem-posing tasks, the solution process of the mathematical modeling question did not change a lot. However, problem-posing activities were observed to have helped some students understand the mathematical modeling question.